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Polyhedra. STEM Cats 2014. Tessellations. M.C. Escher. Buckminsterfullerene. Common Cold Virus. Bogota Sport Center. Epcot. Dice. Seven Days Sci Fi TV Series. Rubies. Giant’s Causeway. Origami. Lamps. Projection of Cube. Projection of a Hypercube. Projection of a Hypercube.

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polyhedra

Polyhedra

STEM Cats 2014

challenge 1
Challenge #1

Construct as many tessellations as you can with identical regular polygons

challenge 2
Challenge #2

Construct as many tessellations as you can with the following properties

  • All tiles are regular polygons
  • There are at least two different kinds of tiles
  • The same sequence of tiles meets around each vertex
challenge 3
Challenge #3

Construct as many polyhedra that you can with the following properties

  • All faces are equilateral triangles
  • All edges bend “outward”– the polyhedron is convex
challenge 4
Challenge #4

Construct as many polyhedra that you can with the following properties

  • All faces are identical regular polygons
  • The same number of faces meet at each vertex (corner)
challenge 5
Challenge #5

Construct as many polyhedra that you can with the following properties

  • All faces are regular polygons
  • There are at least two different kinds of faces
  • The same sequence of faces meets around each vertex
challenge 6
Challenge #6

Find all flat shapes formed by six squares that can be folded up to make a cube.

See also http://erikdemaine.org/metamorphosis/

image sources
Image Sources
  • http://www.georgehart.com/virtual-polyhedra/escher.html
  • http://it.wikipedia.org/wiki/Fullereni#mediaviewer/File:Fullerene-C60.png
  • http://www.lightnessofbeingbook.com/LOBColorPlates/images/Plate03b_IcosVirus.jpg
  • http://www.domusweb.it/en/architecture/2012/01/04/el-bosque-de-la-esperanza.html
  • http://images.frpgames.org/products/product_36488.jpg
  • http://i1.sell.com/u/3H/5G/5BQ/4706433-l.jpg
  • http://images.nationalgeographic.com/wpf/media-live/photos/000/011/cache/rubies_1176_990x742.jpg
  • http://shearings-cdn2.zolvtravel.com/DynamicImages/d510/d510755c6e739c2465038ddea2f849d0_640_480-634873692367638135.jpg
  • http://michal.kosmulski.org/origami/icosidodecahedron-jitterbug.jpg
  • http://media.tumblr.com/tumblr_lefroeVII61qeb9gf.jpg
  • http://www.jeffreyventrella.com/Old_Art/cuboctahedron_big.jpg
  • http://www.wdwinfo.com/Photos/600-spaceship-earth3.jpg
  • http://upload.wikimedia.org/wikipedia/commons/d/d9/Rhombic_dodecahedra.png